MathDB

5

Part of 2021 2nd Memorial "Aleksandar Blazhevski-Cane"

Problems(1)

Interesting geometry. Collinearity

Source: 2nd Memorial Mathematical Competition "Aleksandar Blazhevski - Cane" - Problem 5

1/12/2021
Let △ABC\triangle ABC be a triangle with circumcenter OO. The perpendicular bisectors of the segments OA,OBOA,OB and OCOC intersect the lines BC,CABC,CA and ABAB at D,ED,E and FF, respectively. Prove that D,E,FD,E,F are collinear.
geometrycollinearitycollinearCircumcenterappolonius circlehomothetyperpendicular bisector